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anastassius [24]
2 years ago
13

A right circular cylinder is changing shape. The radius is decreasing at the rate of 2 inches/sec while it's height is increasin

g at the rate of 5 inches/sec. When the radius is 4 inches and the height is 6 inches, how fast is the volume changing? Round your answer to three decimal places
Mathematics
1 answer:
Savatey [412]2 years ago
7 0

Answer:

<h3> 552.640in³/s</h3>

Step-by-step explanation:

Volume of a cylinder is expressed as;

V = \pi r^2 h

\frac{dV}{dt} = \frac{dV}{dr} \frac{dr}{dt} +\frac{dV}{dh} \frac{dh}{dt}

dV/dr = 2πrh

dV/dr = 2π(4)(6)

dV/dr = 48(3.14)

dV/dr = 150.72in³/m

dV/dh = πr²

dV/dh = 3.14(4)²

dV/dh = 50.24

Given

dh/dt = 5in/s

dr/dt = 2in/s

Substitute into the dV/dt

dV/dt = 150.72(2)+50.24(5)

dV/dt = 301.44 + 251.2

dV/dt= 552.640in³/s

The volume is changing at the rate of  552.640in³/s

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Answer:

31.5 in

Step-by-step explanation:

  • Volume of a hemisphere = (2/3)\pir³
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First, find the volume of the scoop using the volume of a hemisphere formula with r = 21:

Volume = (2/3)\pi x 21³ = 6174\pi in³

Now equate the found volume of the scoop to the equation of the volume of a cylinder with r = 14, and solve for h:

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Slope is already given in the question so we only need to solve for the y-intercept.

Slope intercept form: y = mx + b

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1 = -0.6 + b

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Answer:

m<6=77°

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